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Chapter 2 One-Dimensional Kinematics

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Page 1: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Chapter 2

One-Dimensional Kinematics

Page 2: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Kinematics § It is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion.

§  1-Dimensional Kinematics (or 1-Dimensional motion) refers to motion in a straight line.

Page 3: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Before describing motion, you must set up a coordinate system –

define an origin and a positive direction.

x0 x

Page 4: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Distance § The total length traveled by an object.

§ “How far have you walked?” is a typical distance question.

§ The SI unit of distance is the meter (m).

Page 5: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

The distance is the total length of travel; if you drive from your house

to the grocery store and back, you have covered a distance of 8.6 mi.

Page 6: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Displacement (Δx) § The change in the position of a particle is called displacement.

§ Δ is a Greek letter used to represent the words “change in”. Δx therefore means “change in x”. It is always calculated by final value minus initial value.

Page 7: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

• “How far are you from home?” is a typical displacement question. • The SI unit for displacement is the meter. • Calculation of displacement:

• Final position – initial position

0xxx −=Δ

Page 8: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Displacement is the change in position. If you drive from your

house to the grocery store and then to your friend’s house, your

displacement is 2.1 mi and the distance you have traveled is 10.7 mi.

Page 9: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

A

B

50 m displacement

100 m

distance

Distance vs... Displacement

§  A picture can help you distinguish between distance and displacement.

Page 10: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Questions

§  Does the odometer in your car measure distance or displacement?

Page 11: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 12: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: Two tennis players approach the net to congratulate one another after a game. a) Find the distance and displacement of player A. b) Repeat for player B.

A B 5 m 2 m

Page 13: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 14: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: You are driving a car on a circular track of diameter 40 meters. After you have driven around 2 ½ times, how far have you driven, and what is your displacement?

Page 15: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

C = 2πr d = 2r

Page 16: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Average Speed § Average speed describes how

fast a particle is moving. The equation is:

Average speed is always a positive number.

§ where: vav = average speed d = distance Δt = elapsed time § The SI unit of speed is the m/s

txvav Δ

Δ=

Page 17: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Average Velocity § Average velocity describes how fast the displacement is changing. The equation is:

Average velocity is + or – depending on direction.

§ where: vav = average velocity Δx = displacement Δt = elapsed time § The SI unit of velocity is the m/s.

avexvt

Δ=Δ

Page 18: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

If you return to your starting point, your average velocity is zero.

Page 19: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Interpretation of Average Velocity

The same motion, plotted one-dimensionally and as an x vs. t graph:

Page 20: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: How long will it take the sound of the starting gun to reach the ears of the sprinters if the starter is stationed at the finish line for a 100 m race? Assume that sound has a speed of about 340 m/s.

Page 21: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 22: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

t

x Δx

Δt A

B vav = Δx/Δt

Page 23: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem: Determine the average velocity from the graph.

x (m)

Page 24: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

t

x

What kind of motion does this graph represent?

Page 25: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

Can you determine average velocity from the time at point A to the time at point B from this graph?

t

x A B Δx

Δt

vav = Δx/Δt

Page 26: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem: Determine the average velocity between 1 and 4 seconds.

Page 27: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Instantaneous Velocity § The velocity at a single instant in

time. §  If the velocity is uniform, or constant, the

instantaneous velocity is the same as the average velocity.

§  If the velocity is not constant, than the instantaneous velocity is not the same as the average velocity, and we must carefully distinguish between the two.

Page 28: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Instantaneous Velocity

Draw a tangent line to the curve at B. The slope of this line gives the instantaneous velocity at that specific time.

t

x B Δx

Δt

vins = Δx/Δt

Page 29: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

This plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is tangent to the curve.

Page 30: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: Determine the instantaneous velocity at 1.0 second.

Page 31: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Acceleration (a) § Any change in velocity over a period of time is called acceleration.

§  The sign (+ or -) of acceleration indicates its direction.

§  Acceleration can be… § speeding up § slowing down § turning

Page 32: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Questions

§  If acceleration is zero, what does this mean about the motion of an object?

§  Is it possible for a racecar circling a

track to have zero acceleration?

Page 33: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Uniform (Constant) Acceleration §  In Physics B, we will generally assume

that acceleration is constant. §  With this assumption we are free to use

this equation:

§  The SI unit of acceleration is the m/s2.

tvv

tva

Δ

−=

Δ

Δ= 0

Page 34: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Acceleration in 1-D Motion has a sign!

§  If the sign of the velocity and the sign of the acceleration is the same, the object speeds up.

§  If the sign of the velocity and the sign of the acceleration are different, the object slows down.

Page 35: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Cars accelerating or decelerating

Page 36: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

v-versus-t plots with constant acceleration

Page 37: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Qualitative Demonstrations

1)  Demonstrate the motion of a particle that has zero initial velocity and positive acceleration.

2)  Demonstrate the motion of a particle that has zero initial velocity and negative acceleration.

3)  Demonstrate the motion of a particle that has positive initial velocity and negative acceleration.

4)  Demonstrate the motion of a particle that has negative initial velocity and positive acceleration.

Page 38: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: A horse is running with an initial velocity of 11 m/s, and begins to accelerate at –1.81 m/s2. How long does it take the horse to stop?

Page 39: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

Demonstrate the motion of this particle. Is it accelerating?

t (s)

v (m/s) 0.50

Page 40: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

Demonstrate the motion of this particle. Is it accelerating?

t

v

Page 41: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

What physical feature of the graph gives the acceleration?

t

v Δv

Δt A

B a = Δv/Δt

Page 42: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

What physical feature of the graph gives the acceleration?

t

v Δv

Δt A

B a = Δv/Δt

Page 43: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Graphical Problem

What physical feature of the graph gives the Displacement?

t

v A

B Area

Remember to break area into shapes you know

Page 44: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: Determine the acceleration from the graph.

Page 45: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

How would you describe the motion of this particle?

Practice Problem: Determine the displacement of the object from 0 to 4 seconds.

Page 46: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Position vs.... Time Graphs §  Particles moving with no

acceleration (constant velocity) have graphs of position vs.... time with one slope. The velocity is not changing since the slope is constant.

§  Position vs.... time graphs for particles moving with constant acceleration look parabolic. The instantaneous slope is changing. In this graph it is increasing, and the particle is speeding up.

Page 47: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Uniformly Accelerating Objects

§  You see the car move faster and faster. This is a form of acceleration.

§  The position vs.... time graph for the accelerating car reflects the bigger and bigger Δx values.

§  The velocity vs... time graph reflects the increasing velocity.

Page 48: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Describe the motion §  This object is moving in the

positive direction and accelerating in the positive direction (speeding up).

§  This object is moving in the negative direction and accelerating in the negative direction (speeding up).

§  This object is moving in the negative direction and accelerating in the positive direction (slowing down).

Page 49: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Draw Graphs for Stationary Particles

x

t

Position vs... time

v

t

Velocity vs... time

a

t

Acceleration vs... time

Page 50: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Draw Graphs for Constant Non-zero Velocity

x

t

Position vs... time

v

t

Velocity vs... time

a

t

Acceleration vs... time

Page 51: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Draw Graphs for Constant Non-zero Acceleration

x

t

Position vs... time

v

t

Velocity vs... time

a

t

Acceleration vs... time

Page 52: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Kinematic Equations

212

2 20 2 ( )

o

o o

v v atx x v t at

v v a x

= +

= + +

= + Δ

221

0

021

0 )(

attvxxtvvxx

f ++=

++=

Page 53: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: A plane is flying in a northwest direction when it lands, touching the end of the runway with a speed of 130 m/s. If the runway is 1.0 km long, what must the acceleration of the plane be if it is to stop while leaving ¼ of the runway remaining as a safety margin?

Page 54: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 55: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: On a ride called the Detonator at Worlds of Fun in Kansas City, passengers accelerate straight downward from 0 to 20 m/s in 1.0 second. a)  What is the average acceleration of the passengers on this ride?

b)  How fast would they be going if they accelerated for an additional second at this rate?

Page 56: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 57: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem -- continued c) Sketch approximate x-vs.-t, v-vs.-t and a-vs.-t graphs for this ride.

Page 58: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 59: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: Air bags are designed to deploy in 10 ms. Estimate the acceleration of the front surface of the bag as it expands. Express your answer in terms of the acceleration of gravity g.

Page 60: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 61: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and decelerate at 3.5 m/s2. a)  How far do you travel before stopping?

b)  When you have traveled only half the stopping distance, what is your speed?

Page 62: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 63: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem -- continued c)  How long does it take you to stop?

d)  Draw x vs... t, v vs... t, and a vs... t graphs for this.

Page 64: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 65: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Free Fall § When an object is falling under the influence of gravity, with gravity being the only force on the object.

§ Gravity accelerates the object toward the earth the entire time it rises, and the entire time it falls.

Page 66: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

§ The acceleration due to gravity near the surface of the earth has a magnitude of 9.81 m/s2. The direction of this acceleration is DOWN.

§ Air resistance is ignored.

Page 67: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

An object falling in air is subject to air resistance (and therefore is not freely falling).

Page 68: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Free fall from rest:

Page 69: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: You drop a ball from rest off a 120 m high cliff. Assuming air resistance is negligible,

a)  how long is the ball in the air?

b)  what is the ball’s speed and velocity when it strikes the ground at the base of the cliff?

c)  sketch approximate x-vs.-t, v-vs.-t, a-vs.-t graphs for this situation.

Page 70: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 71: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem: You throw a ball straight upward into the air with a velocity of 20.0 m/s, and you catch the ball some time later. a)  How long is the ball in the air?

b)  How high does the ball go?

Page 72: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 73: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Practice Problem -- continued c)  What is the ball’s velocity when you catch it?

d)  Sketch approximate x-vs.-t, v-vs.-t, a-vs.-t graphs for this situation.

Page 74: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous
Page 75: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Symmetry in Free Fall §  When something is thrown straight upward

under the influence of gravity, and then returns to the thrower, this is very symmetric.

§  The object spends half its time traveling up; half traveling down.

§  Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with.

§  Acceleration is 9.8 m/s2 and directed DOWN the entire time the object is in the air!

§  Let’s see some demos!

Page 76: Chapter 2 One-Dimensional Kinematics - Marlington … 1d Lect… ·  · 2012-09-121-Dimensional Kinematics (or 1-Dimensional ... av = average speed d = distance ... Instantaneous

Reflex Testing Lab

§  Using a meter stick, determine your reaction time.